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Questions and Answers
Express 150° into radian measure.
Express 150° into radian measure.
Evaluate $(4i)^2 + 8$.
Evaluate $(4i)^2 + 8$.
The angle 240° lies in which quadrant?
The angle 240° lies in which quadrant?
What is the reference angle of 135°?
What is the reference angle of 135°?
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What is the result of $(3 + 2i) - (1 + 2i)$?
What is the result of $(3 + 2i) - (1 + 2i)$?
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Evaluate $i^{16}$.
Evaluate $i^{16}$.
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What is the value of sin(-30°)?
What is the value of sin(-30°)?
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The expression $\cos^2 \theta + \sin^2 \theta$ is equal to what?
The expression $\cos^2 \theta + \sin^2 \theta$ is equal to what?
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What is the exact value of Sin(-270°)?
What is the exact value of Sin(-270°)?
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What is the exact value of Cos(45°)?
What is the exact value of Cos(45°)?
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What is the result of adding the complex numbers (6 + 4i) and (-2 + i)?
What is the result of adding the complex numbers (6 + 4i) and (-2 + i)?
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What is the result of the operation 2x - 3y if x = 2 + 2i and y = 4i?
What is the result of the operation 2x - 3y if x = 2 + 2i and y = 4i?
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What is the result of multiplying (1 + 2i)(1 - 4i)?
What is the result of multiplying (1 + 2i)(1 - 4i)?
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What is the conjugate of Z = 6 + 2i?
What is the conjugate of Z = 6 + 2i?
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Study Notes
Trigonometry and Complex Numbers Assignment
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Part One: Multiple Choice Questions
- Question 1: Convert 150° to radians. The answer is 5π/6.
- Question 2: Evaluate (4i)² + 8. The answer is -8.
- Question 3: Determine the quadrant of 240°. The answer is the third quadrant.
- Question 4: Find the reference angle of 135°. The answer is 45°.
- Question 5: Calculate (3 + 2i) – (1 + 2i). The answer is 2.
- Question 6: Calculate the hypotenuse of a triangle with sides 8m and 6m. The answer is 10m.
- Question 7: Evaluate i¹⁶. The answer is 1.
- Question 8: Find the value of sin(-30°). The answer is -1/2.
- Question 9: Simplify cos²θ + sin²θ. The answer is 1.
- Question 10: Find the conjugate of (2 – 5i). The answer is (2 + 5i).
Part Two: Structure Questions
- Question 1: Calculate the six trigonometric functions (sin, cos, tan, cot, csc, sec) for the acute angle of a triangle with sides 3m and 4m. (no specific answers are given for this question in the image)
- Question 2: Convert 90° and 360° to radians.
- Question 3: Convert given radian values to degrees.
- Question 4: Find the reference angles for 60°, 225°, 315° and 120°.
Part Three: Identities
- Question 4: Prove trigonometric identities (tanθ cotθ = 1, etc.)
Part Four: Trigonometric Graphs
- Question 5: Sketch the graphs of sine, cosine, tangent, cotangent, secant, and cosecant functions for 0° ≤ x ≤ 360°.
Part Five: Complex Numbers
- Question 5: Add, subtract, and multiply/divide complex numbers. Example given: (6+4i) + (-2+i) equals (4+5i). Other examples included include various operations.
- Question 5: Calculate the values of trigonometric functions in complex numbers with degrees (eg, cos(45°)). Various examples included with degrees or other mathematical operations.
Simplification and Conjugate of Complex Numbers.
- Examples: Calculate the values for specific complex numbers in various ways.
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Description
Test your knowledge with this assignment focused on trigonometry and complex numbers. It includes multiple choice questions on angle conversions, evaluating complex expressions, and understanding trigonometric functions. Perfect for anyone looking to strengthen their skills in these mathematical topics.
